Then the inference is that it would touch both?
But what do you say to a new point of view? Must not that which is
to touch another be next to that which it is to touch, and occupy
the place nearest to that in which what it touches is situated?
Then the one, if it is to touch itself, ought to be situated next to
itself, and occupy the place next to that in which itself is?
And that would require that the one should be two, and be in two
places at once, and this, while it is one, will never happen.
Then the one cannot touch itself any more than it can be two?
Neither can it touch others.
The reason is, that whatever is to touch another must be in
separation from, and next to, that which it is to touch, and no
third thing can be between them.
Two things, then, at the least ate necessary to make contact
And if to the two a third be added in due order, the number of terms
will be three, and the contacts two?
And every additional term makes one additional contact, whence it
follows that the contacts are one less in number than the terms; the
first two terms exceeded the number of contacts by one, and the
whole number of terms exceeds the whole number of contacts by one in
like manner; and for every one which is afterwards added to the number